Let D ⊂ C n be a smoothly bounded pseudoconvex Levi corank one domain with defining function r, i.e., the Levi form ∂∂r of the boundary ∂D has at least (n − 2) positive eigenvalues everywhere on ∂D. The main goal of this article is to obtain bounds for the Carathéodory, Kobayashi and the Bergman distance between a given pair of points p, q ∈ D in terms of parameters that reflect the Levi geometry of ∂D and the distance of these points to the boundary. Applications include an understanding of Fridman's invariant for the Kobayashi metric on Levi corank one domains, a description of the balls in the Kobayashi metric on such domains that are centered at points close to the boundary in terms of Euclidean data and the boundary behaviour of Kobayashi isometries from such domains.

Background: Virtual reality (VR) has been established as a valuable tool outside of medicine but there has been limited uptake in orthopaedics despite being a specialty heavily dependent on psychomotor skills. The purpose of this study was to assess the feasibility of setting up an on-site virtual reality surgical training hub for an orthopaedic surgery unit. A secondary objective was to document encountered hurdles to assist other institutions with a similar process. Methods: The study explored the logistical and organizational considerations in the process of creating a virtual reality training area. This included: review of location, set up management, funding arrangements, set up time, research opportunities and training time. Set up and completion times were recorded during a separate trial of 24 participants ranging from medical students to senior consultant orthopaedic surgeons. Results: A VR training area was successfully established over a period of 3 months. A dedicated area for training where the equipment remains permanently was designated to facilitate ease of use. Average set up took 7.5 min to turn the computer on and 25 min for the participants to start the module. Issues identified during set up were recorded. Conclusions:The study demonstrated that it is possible to set up a dedicated area for virtual reality surgical training within a hospital unit. A dedicated lockable area is the most feasible method of establishing such a space and reduces the requirement to recalibrate and transfer equipment around the hospital.

We study the Wu metric for the non-convex domains of the formwhere 0 < m < 1/2. Explicit expressions for the Kobayashi metric and the Wu metric on such pseudo-eggs E2m are obtained. The Wu metric is then verified to be a continuous Hermitian metric on E2m which is real analytic everywhere except along the complex hypersurface Z = {(0, z2, . . . , zn) ∈ E2m}. We also show that the holomorphic sectional curvature of the Wu metric for this non-compact family of pseudoconvex domains is bounded above in the sense of currents by a negative constant independent of m. This verifies a conjecture of S. Kobayashi and H. Wu for such E2m.1991 Mathematics Subject Classification. Primary: 32F45; Secondary: 32Q45, 32H15.

The purpose of this article is to study Lipschitz CR mappings from an h-extendible (or semi-regular) hypersurface in C n . Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved.Abstract. The purpose of this article is to study Lipschitz CR mappings from an h-extendible (or semi-regular) hypersurface in C n . Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved.

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